Journal of Function Spaces The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Molecular Characterization of Hardy Spaces Associated with Twisted Convolution Tue, 22 Jul 2014 06:54:01 +0000 We give a molecular characterization of the Hardy space associated with twisted convolution. As an application, we prove the boundedness of the local Riesz transform on the Hardy space. Jizheng Huang and Yu Liu Copyright © 2014 Jizheng Huang and Yu Liu. All rights reserved. Estimates of Intrinsic Square Functions on Generalized Weighted Morrey Spaces Tue, 22 Jul 2014 06:49:15 +0000 We prove the boundedness of the intrinsic functions on generalized weighted Morrey spaces , including the strong type estimates and weak type estimates. Moreover, we define the kth-order commutators generated by functions and intrinsic functions, and obtain their strong type estimates on . In some cases, we improve previous results. Guilian Gao and Xiaomei Wu Copyright © 2014 Guilian Gao and Xiaomei Wu. All rights reserved. Smooth Decompositions of Triebel-Lizorkin and Besov Spaces on Product Spaces of Homogeneous Type Tue, 22 Jul 2014 06:37:06 +0000 We introduce Triebel-Lizorkin and Besov spaces by Calderón’s reproducing formula on product spaces of homogeneous type. We also obtain smooth atomic and molecular decompositions for these spaces. Fanghui Liao, Zongguang Liu, and Xiaojin Zhang Copyright © 2014 Fanghui Liao et al. All rights reserved. On Convergence of Fixed Points in G-Complete Fuzzy Metric Spaces Sun, 20 Jul 2014 12:38:28 +0000 We provide some results on the convergence of the sequence of fixed points for some different sequences of contraction mappings or fuzzy metrics in G-complete fuzzy metric spaces with the H-type t-norms. We improve the corresponding conclusions in the literature. Dong Qiu and Shuai Deng Copyright © 2014 Dong Qiu and Shuai Deng. All rights reserved. A Modified Analytic Function Space Feynman Integral and Its Applications Sun, 20 Jul 2014 06:56:08 +0000 We analyze the generalized analytic function space Feynman integral and then defined a modified generalized analytic function space Feynman integral to explain the physical circumstances. Integration formulas involving the modified generalized analytic function space Feynman integral are established which can be applied to several classes of functionals. Seung Jun Chang, Jae Gil Choi, and Hyun Soo Chung Copyright © 2014 Seung Jun Chang et al. All rights reserved. Remarks on the Unimodular Fourier Multipliers on α-Modulation Spaces Thu, 17 Jul 2014 07:24:24 +0000 We study the boundedness properties of the Fourier multiplier operator on -modulation spaces and Besov spaces . We improve the conditions for the boundedness of Fourier multipliers with compact supports and for the boundedness of on . If is a radial function and satisfies some size condition, we obtain the sufficient and necessary conditions for the boundedness of between and . Guoping Zhao, Jiecheng Chen, and Weichao Guo Copyright © 2014 Guoping Zhao et al. All rights reserved. Multilinear Singular Integral Operators on Generalized Weighted Morrey Spaces Thu, 17 Jul 2014 06:55:12 +0000 The purpose of this paper is to discuss the boundedness properties of multilinear Calderón-Zygmund operator and its commutator on the generalized weighted Morrey spaces. Yue Hu, Zhang Li, and Yueshan Wang Copyright © 2014 Yue Hu et al. All rights reserved. Existence and Asymptotic Stability of Solutions of a Functional Integral Equation via a Consequence of Sadovskii’s Theorem Wed, 16 Jul 2014 00:00:00 +0000 Using the technique of measures of noncompactness and, in particular, a consequence of Sadovskii’s fixed point theorem, we prove a theorem about the existence and asymptotic stability of solutions of a functional integral equation. Moreover, in order to illustrate our results, we include one example and compare our results with those obtained in other papers appearing in the literature. Agnieszka Chlebowicz, Mohamed Abdalla Darwish, and Kishin Sadarangani Copyright © 2014 Agnieszka Chlebowicz et al. All rights reserved. On Monotonic and Nonnegative Solutions of a Nonlinear Volterra-Stieltjes Integral Equation Wed, 09 Jul 2014 08:57:50 +0000 We study the existence of monotonic and nonnegative solutions of a nonlinear quadratic Volterra-Stieltjes integral equation in the space of real functions being continuous on a bounded interval. The main tools used in our considerations are the technique of measures of noncompactness in connection with the theory of functions of bounded variation and the theory of Riemann-Stieltjes integral. The obtained results can be easily applied to the class of fractional integral equations and Volterra-Chandrasekhar integral equations, among others. Tomasz Zając Copyright © 2014 Tomasz Zając. All rights reserved. Asymptotic Study of the 2D-DQGE Solutions Mon, 07 Jul 2014 09:31:27 +0000 We study the regularity of the solutions of the surface quasi-geostrophic equation with subcritical exponent . We prove that if the initial data is small enough in the critical space , then the regularity of the solution is of exponential growth type with respect to time and its norm decays exponentially fast. It becomes then infinitely differentiable with respect to time and has value in all homogeneous Sobolev spaces for . Moreover, we give some general properties of the global solutions. Jamel Benameur and Mongi Blel Copyright © 2014 Jamel Benameur and Mongi Blel. All rights reserved. Hyers-Ulam Stability of Differentiation Operator on Hilbert Spaces of Entire Functions Sun, 06 Jul 2014 09:11:46 +0000 We investigate the Hyers-Ulam stability of differentiation operator on Hilbert spaces of entire functions. We give a necessary and sufficient condition in order that the operator has the Hyers-Ulam stability and also show that the best constant of Hyers-Ulam stability exists. Chun Wang and Tian-Zhou Xu Copyright © 2014 Chun Wang and Tian-Zhou Xu. All rights reserved. Change of Scale Formulas for Wiener Integrals Related to Fourier-Feynman Transform and Convolution Thu, 26 Jun 2014 11:42:39 +0000 Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in Banach algebra on classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel class and in a generalized Fresnel class on abstract Wiener space. We express Fourier-Feynman transform and convolution product of functionals in as limits of Wiener integrals. Moreover we obtain change of scale formulas for Wiener integrals related to Fourier-Feynman transform and convolution product of these functionals. Bong Jin Kim, Byoung Soo Kim, and Il Yoo Copyright © 2014 Bong Jin Kim et al. All rights reserved. Function Spaces and Operators with Applications Sun, 22 Jun 2014 08:28:27 +0000 Yongqiang Fu, Qingying Bu, Donghai Ji, and Lars Diening Copyright © 2014 Yongqiang Fu et al. All rights reserved. Atomic Decomposition of Weighted Lorentz Spaces and Operators Thu, 19 Jun 2014 09:31:11 +0000 We obtain an atomic decomposition of weighted Lorentz spaces for a class of weights satisfying the Δ2 condition. Consequently, we study operators such as the multiplication and composition operators and also provide Hölder’s-type and duality-Riesz type inequalities on these weighted Lorentz spaces. Eddy Kwessi, Geraldo de Souza, Fidele Ngwane, and Asheber Abebe Copyright © 2014 Eddy Kwessi et al. All rights reserved. Asymptotically Stable Solutions of a Generalized Fractional Quadratic Functional-Integral Equation of Erdélyi-Kober Type Mon, 16 Jun 2014 09:17:50 +0000 We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach space . We show that this equation has at least one asymptotically stable solution. Mohamed Abdalla Darwish and Beata Rzepka Copyright © 2014 Mohamed Abdalla Darwish and Beata Rzepka. All rights reserved. Fixed Point Theorems for Contractions of Rational Type with PPF Dependence in Banach Spaces Mon, 09 Jun 2014 12:56:14 +0000 We prove the existence of the PPF dependent fixed point in the Razumikhin class for contractions of rational type in Banach spaces, by using a general class of pairs of functions. Our result has as particular cases a great number of interesting consequences which extend and generalize some results appearing in the literature. J. Rocha, B. Rzepka, and K. Sadarangani Copyright © 2014 J. Rocha et al. All rights reserved. Compactness of the Commutator of Multilinear Fourier Multiplier Operator on Weighted Lebesgue Space Sun, 01 Jun 2014 00:00:00 +0000 Let be the multilinear Fourier multiplier operator associated with multiplier satisfying the Sobolev regularity that for some . The authors prove that if and , then the commutator is bounded from to . Moreover, the authors also prove that if and , then the commutator is compact operator from to . Jiang Zhou and Peng Li Copyright © 2014 Jiang Zhou and Peng Li. All rights reserved. Nonlinear Systems in Function Spaces and Applications in Biomedical Sciences, Control Theory, and Engineering Wed, 28 May 2014 11:08:51 +0000 Jin Liang, C. Cuevas, T. Diagana, G. N’Guérékata, and M. Van Nguyen Copyright © 2014 Jin Liang et al. All rights reserved. Local Morrey and Campanato Spaces on Quasimetric Measure Spaces Sun, 25 May 2014 11:46:48 +0000 We define and investigate generalized local Morrey spaces and generalized local Campanato spaces, within a context of a general quasimetric measure space. The locality is manifested here by a restriction to a subfamily of involved balls. The structural properties of these spaces and the maximal operators associated to them are studied. In numerous remarks, we relate the developed theory, mostly in the “global” case, to the cases existing in the literature. We also suggest a coherent theory of generalized Morrey and Campanato spaces on open proper subsets of . Krzysztof Stempak and Xiangxing Tao Copyright © 2014 Krzysztof Stempak and Xiangxing Tao. All rights reserved. Commutators of Multilinear Calderón-Zygmund Operator and BMO Functions in Herz-Morrey Spaces with Variable Exponents Sun, 25 May 2014 11:02:21 +0000 We obtain the boundedness of a commutator generated by multilinear Calderón-Zygmund operator and BMO functions in Herz-Morrey spaces with variable exponents. Canqin Tang, Qing Wu, and Jingshi Xu Copyright © 2014 Canqin Tang et al. All rights reserved. The Solution of Nonlinear Fourth-Order Differential Equation with Integral Boundary Conditions Tue, 20 May 2014 12:15:11 +0000 An iterative algorithm is proposed for solving the solution of a nonlinear fourth-order differential equation with integral boundary conditions. Its approximate solution is represented in the reproducing kernel space. It is proved that converges uniformly to the exact solution . Moreover, the derivatives of are also convergent to the derivatives of . Numerical results show that the method employed in the paper is valid. Yanli Fu and Huanmin Yao Copyright © 2014 Yanli Fu and Huanmin Yao. All rights reserved. Boundedness of Oscillatory Hyper-Hilbert Transform along Curves on Sobolev Spaces Mon, 19 May 2014 09:33:16 +0000 The oscillatory hyper-Hilbert transform along curves is of the following form: , where , , and . The study on this operator is motivated by the hyper-Hilbert transform and the strongly singular integrals. The bounds for have been given by Chen et al. (2008 and 2010). In this paper, for some , , and , the boundedness of on Sobolev spaces and the boundedness of this operator from to are obtained. Jun Li and Guilian Gao Copyright © 2014 Jun Li and Guilian Gao. All rights reserved. Morrey Spaces and Related Function Spaces Mon, 19 May 2014 08:36:34 +0000 Yoshihiro Sawano, Hendra Gunawan, Vagif Guliyev, and Hitoshi Tanaka Copyright © 2014 Yoshihiro Sawano et al. All rights reserved. Projection Methods for a System of Nonlinear Mixed Variational Inequalities in Banach Spaces Thu, 15 May 2014 07:01:19 +0000 The existence and uniqueness of solution for a system of nonlinear mixed variational inequality in Banach spaces is given firstly. A Mann iterative sequences with errors for this system of nonlinear mixed variational inequalities in Banach spaces is studied, by using the generalized f-projection operator . Our results extend the main results in (Verma (2005); Verma (2001)) from Hilbert spaces to Banach spaces. Zhong-Bao Wang, Guo-Ji Tang, and Hong-Ling Zhang Copyright © 2014 Zhong-Bao Wang et al. All rights reserved. Matrix Transformations, Measures of Noncompactness, and Applications Tue, 13 May 2014 12:39:26 +0000 S. A. Mohiuddine, Józef Banaś, M. Mursaleen, Richard F. Patterson, Abdullah Alotaibi, and Asadollah Aghajani Copyright © 2014 S. A. Mohiuddine et al. All rights reserved. The Boundedness of Marcinkiewicz Integral Associated with Schrödinger Operator and Its Commutator Thu, 08 May 2014 13:05:02 +0000 The authors prove that Marcinkiewicz integral operator is not only are bounded on , for , but also a bounded map from to weak . Meanwhile, the -boundedness and -boundedness are also obtained. Finally, the -boundedness and -boundedness for the commutator of Marcinkiewicz integral of schrödinger type are established. Dongxiang Chen and Dan Zou Copyright © 2014 Dongxiang Chen and Dan Zou. All rights reserved. Approximate Homomorphisms and Derivations on Normed Lie Triple Systems Wed, 07 May 2014 12:23:16 +0000 We investigate the generalized Hyers-Ulam stability of homomorphisms and derivations on normed Lie triple systems for the following generalized Cauchy-Jensen additive equation , where are nonzero real numbers. As a results, we generalize some stability results concerning this equation. Hark-Mahn Kim and Juri Lee Copyright © 2014 Hark-Mahn Kim and Juri Lee. All rights reserved. On Distance Function in Some New Analytic Bergman Type Spaces in Tue, 06 May 2014 12:47:12 +0000 We extend our previous sharp results on distances obtained for analytic Bergman type spaces in unit disk to some new analytic Bergman type spaces in higher dimensions in . Also, we study the same problem in anisotropic mixed norm spaces consisting of -harmonic functions on the unit polydisc of . Romi F. Shamoyan and Olivera R. Mihić Copyright © 2014 Romi F. Shamoyan and Olivera R. Mihić. All rights reserved. Recent Advances in Inequalities and -Harmonic Equations Tue, 06 May 2014 12:40:19 +0000 Shusen Ding, Peilin Shi, and Yuming Xing Copyright © 2014 Shusen Ding et al. All rights reserved. Advances in Study of Poincaré Inequalities and Related Operators Tue, 06 May 2014 07:35:39 +0000 We will present an up-to-date account of the recent advances made in the study of Poincaré inequalities for differential forms and related operators. Yuming Xing and Shusen Ding Copyright © 2014 Yuming Xing and Shusen Ding. All rights reserved.